TY - JOUR
T1 - Elementary proofs of grothendieck theorems for completely bounded norms
AU - Regev, Oded
AU - Vidick, Thomas
N1 - Publisher Copyright:
© Copyright by THETA, 2014.
PY - 2014
Y1 - 2014
N2 - We provide alternative proofs of two recent Grothendieck theorems for jointly completely bounded bilinear forms, originally due to Pisier and Shlyakhtenko (Grothendieck's theorem for operator spaces, Invent. Math. 150(2002), 185-217) and Haagerup and Musat (The Effros-Ruan conjecture for bilinear forms on C*-algebras, Invent. Math. 174(2008), 139-163). Our proofs are elementary and are inspired by the so-called embezzlement states in quantum information theory. Moreover, our proofs lead to quantitative estimates.
AB - We provide alternative proofs of two recent Grothendieck theorems for jointly completely bounded bilinear forms, originally due to Pisier and Shlyakhtenko (Grothendieck's theorem for operator spaces, Invent. Math. 150(2002), 185-217) and Haagerup and Musat (The Effros-Ruan conjecture for bilinear forms on C*-algebras, Invent. Math. 174(2008), 139-163). Our proofs are elementary and are inspired by the so-called embezzlement states in quantum information theory. Moreover, our proofs lead to quantitative estimates.
KW - Bilinear form
KW - Completely bounded norm
KW - Grothendieck inequality
KW - Quantum information theory
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U2 - 10.7900/jot.2012jul02.1947
DO - 10.7900/jot.2012jul02.1947
M3 - Article
AN - SCOPUS:84920265166
SN - 0379-4024
VL - 71
SP - 491
EP - 506
JO - Journal of Operator Theory
JF - Journal of Operator Theory
IS - 2
ER -